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79 Superplasticity of highly disclinated graphene © d v a n c e d S t u d y e n t e r o L t d Rev. Adv. Mater. Sci. 47 (2016) 79-85 Corresponding author: I.A. Ovidko, e-mail: [email protected] SUPERPLASTICITY OF HIGHLY DISCLINATED GRAPHENE A.S. Kochnev 1,2 v i d k o 1,2,3 and B. N. Semenov 1,2,3 1 Peter the Great St. Petersburg Polytechnic University, St. Petersburg 195251, Russia 2 St. Petersburg State University, St. Petersburg 199034, Russia 3 Institute of Problems of Mechanical Engineering, Russian Academy of Sciences, St. Petersburg 199178, Russia Received: November 10, 2016 Abstract. e f o r m a t i o n a n d f r a c t u r e p r o c e s s e s i n h i g h l y d i s c l i n a t e d g r a p h e n e g r a p h e n e containing a high-density ensemble of rectangular disclination quadrupoles - are examined by molecular dynamics simulations. A special disclination mechanism of plastic deformation in graphene is discussed. Also, we consider the effects of disclination-induced curvature in graphene on its mechanical characteristics, namely stress-strain dependence, elastic limit, strain-to-failure and tensile strength. In particular, our simulations reveal that the highly disclinated graphene exhibits superplasticity specified by strain-to-failure 234%. The key reason of superplasticity is in the presence of pre-existent disclinations that enhance generation of new disclination dipoles and other disclination configurations carrying plastic flow in graphene. 1. INTRODUCTION r a p h e n e a c a r b o n m o n o l a y e r w i t h t h e c o v a l e n t l y b o n d e d h e x a g o n a l c r y s t a l s t r u c t u r e s h o w s t h e unique electronic, energy-storage, thermal and mechanical properties being of tremendous interest for a wide range of technologies; see, e.g., reviews [1-10]. For instance, following the experimental data [11], pristine graphene is specified by such outstanding mechanical characteristics as superior intrinsic strength of 130 GPa, superior elastic strain of 25% and extraordinarily high Young modulus of 1.0 TPa. These characteristics are crucially important for structural applications of graphene and its exploitation in nanoelectronics where its mechanical properties are critical for lifetime of graphene-based devices. Also, graphene demonstrates the excellent electronic properties due to its 2D hexagonal crystal structure and the presence of charge carriers that behave like massless particles [1,4,6]. One of the most effective approaches to modify, design and control the remarkable electronic properties of graphene is based on their sensitivity to local curvature and associated elastic strains in graphene; see, e.g., [12-17]. For instance, the pronounced sensitivity of the electronic properties exhibited by graphene to curvature-produced strains in its structure distinctly manifests itself in the giant strain- induced pseudo-magnetic field in graphene nanobubbles [14]. The experiment [14] under discussion is a good example of tuning and controlling the electronic properties of graphene through its curvature engineering. At the same time, research efforts addressing the effects of curvature on the mechanical properties of graphene are very limited [19-21]. In particular, in paper [19], graphene with a high-density ensemble of homogeneously dispersed topological disclinations was defined and theoretically described as a new two-dimensional material called highly disclinated graphene (HDG). Following [19], 5- and d i s c l i n a t i o n s p e n t a g o n a n d h e p t a g o n r i n g s o f c a r b o n a t o m s i n h e x a g o n a l l a t t i c e o f g r a p h e n e

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Page 1: SUPERPLASTICITY OF HIGHLY DISCLINATED GRAPHENE · Superplasticity of highly disclinated graphene 81 Fig. 2. Highly disclinated graphene represents a graphene monolayer containing

79Superplasticity of highly disclinated graphene

© 2016 Advanced Study Center Co. Ltd.

Rev. Adv. Mater. Sci. 47 (2016) 79-85

Corresponding author: I.A. Ovidko, e-mail: [email protected]

SUPERPLASTICITY OF HIGHLY DISCLINATED GRAPHENE

A.S. Kochnev1,2, I. A. Ovid’ko1,2,3 and B. N. Semenov1,2,3

1Peter the Great St. Petersburg Polytechnic University, St. Petersburg 195251, Russia2St. Petersburg State University, St. Petersburg 199034, Russia

3Institute of Problems of Mechanical Engineering, Russian Academy of Sciences,St. Petersburg 199178, Russia

Received: November 10, 2016

Abstract.  Deformation  and  fracture  processes  in  highly  disclinated  graphene  –  graphenecontaining a high-density ensemble of rectangular disclination quadrupoles - are examined bymolecular dynamics simulations. A special disclination mechanism of plastic deformation ingraphene is discussed. Also, we consider the effects of disclination-induced curvature in grapheneon its mechanical characteristics, namely stress-strain dependence, elastic limit, strain-to-failureand tensile strength. In particular, our simulations reveal that the highly disclinated grapheneexhibits superplasticity specified by strain-to-failure 234%. The key reason of superplasticity isin the presence of pre-existent disclinations that enhance generation of new disclination dipolesand other disclination configurations carrying plastic flow in graphene.

1. INTRODUCTION

Graphene – a carbon monolayer with the covalentlybonded hexagonal crystal structure – shows  theunique electronic, energy-storage, thermal andmechanical properties being of tremendous interestfor a wide range of technologies; see, e.g., reviews[1-10]. For instance, following the experimental data[11], pristine graphene is specified by suchoutstanding mechanical characteristics as superiorintrinsic strength of 130 GPa, superior elastic strainof 25% and extraordinarily high Young modulus of 1.0 TPa. These characteristics are cruciallyimportant for structural applications of graphene andits exploitation in nanoelectronics where itsmechanical properties are critical for lifetime ofgraphene-based devices.

Also, graphene demonstrates the excellentelectronic properties due to its 2D hexagonal crystalstructure and the presence of charge carriers thatbehave like massless particles [1,4,6]. One of themost effective approaches to modify, design and

control the remarkable electronic properties ofgraphene is based on their sensitivity to localcurvature and associated elastic strains in graphene;see, e.g., [12-17]. For instance, the pronouncedsensitivity of the electronic properties exhibited bygraphene to curvature-produced strains in itsstructure distinctly manifests itself in the giant strain-induced pseudo-magnetic field in graphenenanobubbles [14]. The experiment [14] underdiscussion is a good example of tuning andcontrolling the electronic properties of graphenethrough its curvature engineering.

At the same time, research efforts addressingthe effects of curvature on the mechanical propertiesof graphene are very limited [19-21]. In particular, inpaper [19], graphene with a high-density ensembleof homogeneously dispersed topologicaldisclinations was defined and theoretically describedas a new two-dimensional material called highlydisclinated graphene (HDG). Following [19], 5- and7-disclinations – pentagon and heptagon rings ofcarbon atoms – in hexagonal lattice of graphene

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80 A.S. Kochnev, I.A. Ovid’ko and B.N. Semenov

create the nanoscopically buckled structurecontaining local “hills” and “valleys”. It is theoreticallypredicted that the buckled structure may causepotentially excellent mechanical characteristics ofHDG. The main aim of this paper is to examine bymolecular dynamics (MD) simulations bothdeformation and fracture processes in HDG with aspecial attention being devoted to the curvatureeffects in HDG on its mechanical characteristics,such as stress-strain dependence, elastic limit,strain-to-failure and tensile strength. In particular,our simulations reveal a very intriguing and practicallyimportant feature of the deformation behaviorexhibited by HDG, namely its superplasticityspecified by strain-to-failure 234%.

2. SIMULATION METHODS

In description of deformation and fracture processesin HDG, we used the Large-scale Atomic/MolecularMassively Parallel Simulator MD simulationpackage. In order to specify interatomic bonds, theadaptive intermolecular reactive bond order(AIREBO) potential [22] is utilized which isconventionally exploited in computer models ofdeformation and fracture processes in graphenematerials; see, e.g., [21,23-29].

The 3D simulation cell contains 120 carbonatoms and is specified by periodic boundary

conditions along vertical and horizon directions inFig. 1. At the first stage of the pre-simulationprocedure, we create a flat HDR specimencontaining a regular lattice of rectangularquadrupoles of 5- and 7-disclinations in thehexagonal lattice of graphene (Fig. 1). Disclinationsbelonging to a quadrupole in HDG generate high in-plane stresses localized in the vicinity of thequadrupole. (Disclination quadrupoles do notgenerate long-range stresses, because stress fieldsof 5- and 7-disclinations belonging to one quadrupoleare mutually screened [19], as with discinationquadrupoles in 3D solids [30,31].) In thesecircumstances, HDG in its flat state contains highlydistorted hexagon cells of carbon atoms (Fig. 1).The 3D simulation cell of HDG in its initial (pre-deformation) flat state has the length of 17.7 Å andwidth of 17.5 Å.The distance between carbon atomsin graphene in its initial state is taken as 1.42 Å.

At the second stage of the pre-simulationprocedure, the initial flat HDG model was relaxedthrough simulations involving 1,000,000 iterationsteps in Nose-Hoover thermostat at roomtemperature (300K). As a result of the relaxationprocedure, the initially flat GNR is transformed intoa nanoscopically buckled structure containing local“hills”  and  “valleys”  associated with  5-  and  7-disclinations, respectively (Fig. 2). The reason forgeneration of curvature in the HDG (Fig. 2) is relatedto balance between elastic energies that specifyflat and curved configurations of graphene containingdisclinations [19]. In short, in the absence of externalmechanical load, the elastic energy of HDG in itscurved configuration (Fig. 2) is much lower than thatin its flat counterpart. With this factor, the HDG tendsto be curved (Fig. 2) when external mechanical loadis absent.

Then the tensile strain was applied with a strainrate of 0.0005 per femtosecond. The tension isapplied along the horizontal direction in plane shownin Fig. 1. Evolution of the HDG structure undertensile deformation will be considered in detail innext section. In doing so, illustrative figures will bepresented showing projection of the HSD structureonto plane where its initial flat state was pre-simulated (Fig. 1).

3. DEFECTS, DEFORMATION ANDFRACTURE PROCESSES INHIGHLY DEFECTED GRAPHENE

The HDG (Fig. 2) represents a good example ofgraphene nanostructures in which the curvatureeffects on mechanical properties of graphene

Fig. 1. Simulation cell of highly disclinated graphenecontains a quadrupole of 5- and 7-disclinations(pentagon and heptagon rings of carbon atoms,respectively) in hexagonal lattice of graphene. 5-and 7-disclinations are colored by blue and green,respectively.

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81Superplasticity of highly disclinated graphene

Fig. 2. Highly disclinated graphene represents a graphene monolayer containing a high-density ensembleof rectangular disclination quadrupoles after relaxation. (a) General 3D view. The relaxed structure of highlydisclinated graphene contains local “hills” and “valleys” associated with 5- and 7-disclinations, respectively.(b) 2D projection of the relaxed structure of highly disclinated graphene.

(a)

(b)

effectively come into play. In order to identify anddescribe such effects, we simulate tensile test ofbuckled HDG. Our MD simulations show that thecurved HDG is, in part, flattened under tension load.In this case, the bending energy accumulated inHDG is, in part, transformed into the stretchingenergy, and in-plane stresses of the disclinationsbecome pronounced. Also, the mechanical loadinduces generation of new 5- and 7-disclinations aswell as crack-like n-cells, that is, n-membered ringsof carbon atoms, where n > 7 (Fig.3.). Moreprecisely, HDG shown in Fig. 3 contains crack-liken-cells specified by n = 8, 11, and 13. Crack-likecells are generated through breaks of interatomicC-C bonds which are typically located at 5- or 7-

disclinations or other crack-like cells (becauseorientations of such bonds deviate from those of thestrongest C-C bonds characterizing regular, 6-membered rings of carbon atoms in graphene). Forinstance, each of crack-like 11-cells (Fig. 3) isgenerated through break of the C-C bond belongingto neighbouring 5- and 7-disclinations or, in otherwords, through convergence of these disclinations.Crack-like 13-cell (Fig. 3) is generated through breakof the C-C bond belonging to two neighbouring 7-disclinations or, in other words, through convergenceof these disclinations.

Further elongation of HDG under tension load isaccompanied by generation of new n-disclinationsand their convergence (that gives rise to an increase

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82 A.S. Kochnev, I.A. Ovid’ko and B.N. Semenov

in an average value of n) in HDG (Fig. 4). Theseprocesses result in the formation of nanoscalecracks/pores that separate HDG into two piecesjoined by a monatomic carbon chain (Fig. 5). Withfurther elongation, a break of the monatomic carbonchain occurs (Fig. 6) which realizes complete failure,that is, complete separation of HDG into twoseparate pieces.

Let us discuss the roles of n-disclinations inplastic deformation and fracture processes occurringin HDG. First, note that point n-disclinations in 2Dgraphene serve as analogues of line disclinations inconventional 3D materials where dipoles of theseline disclinations effectively carry plastic flow; see,e.g., [31-35]. In particular, dipoles and otherconfigurations of line disclinations can significantlycontribute to plastic deformation of nanocrystalline3D materials [31-35]. In the context discussed, it islogical to think that dipoles and other configurations

Fig. 3. Deformed cell of highly disclinated graphene at strain = 55%. New n-disclinations (that are differentfrom initial ones) are coloured yellow and specified by their non-six numbers n.

Fig. 4. Deformed cell of highly disclinated graphene at strain = 85%. The cell contains very large pores.

of n-disclinations are capable of carrying plasticdeformation in graphene. This statement is wellconsistent with both the experimental observationof plastic deformation carried by dislocations(disclination dipoles) in graphene [32] and thecomputer simulations demonstrating that n-disclinations are intensively generated during plasticdeformation of graphene [21,40,41].

Let us consider the situation where no atomsare removed from a mechanically loaded graphenespecimen and no new atoms are added to such aspecimen. In the situation under consideration, onecan distinguish the two basic processes related totransformations of interatomic (C-C) bonds, evolutionof n-disclinations, and associated deformation andfracture events in graphene. These processes arere-arrangements (flip events) and irreversibledebondings (break events) of C-C bonds.

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83Superplasticity of highly disclinated graphene

Fig. 5. Deformed cells of highly disclinated graphene at strain = 224%. (For clarity, two simulation cellsare shown.) Deformation gives rise to separation of each graphene cell into two pieces joined by a monatomiccarbon chain.

Fig. 6. Complete fracture occurs at = 234%.

Flip events are recognized as elementary eventsof plastic deformation in carbon nanotubes [36] andgraphene [37]. For instance, flip events (rotations ofC-C bonds) in hexagonal crystal lattices of grapheneand carbon nanotubes create Stone-Wales defects(quadrupoles of neighbouring 5- and 7-disclinations)and provide slip of dislocations (dipoles of 5- and 7-disclinations) [36,37], that is, in our terms, plasticflow through motion of disclination dipoles.

Irreversible break events destroy interatomic C-C bonds and do not create new C-C bonds inmechanically loaded graphene. In the contextdiscussed, irreversible break events are treated aselementary events of fracture/pre-fracture processesin graphene.

4. STRESS-STRAIN DEPENDENCE

Also, with the MD simulations, we revealed stress-strain dependence (Fig. 7), fracture strain and tensilestrength that characterize HDG. The stress-straincurve (Fig. 7) has the elastic stage when the strain ranges from 0% to the elastic limit

el 40 % (Fig.

7). It is a rather high value; it is larger than the elasticlimit ( 25%) that has been documented in theexperiment [11] with micron-sized pristine graphenemembrane. Also, there is the plastic deformationstage where the stress-strain curve is serrated (Fig.7). In doing so, each drop at the stress-strain curveis related to a non-elastic event - either flip orirreversible debonding of a C-C interatomic bond - inHDR under tension. The plastic deformation stage

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84 A.S. Kochnev, I.A. Ovid’ko and B.N. Semenov

is extended very much (when strain ranges from 40 to 234%) and thus indicates on superplasticityof HDG. (It is dramatically contrasted to brittlebehaviour typically exhibited by pristine and othergraphene structures.) At the same time, the strengthof HDG has value ( 50 GPa; see Fig. 7) being muchlower than the experimentally measured [11] strength( 130 GPa) of pristine graphene membrane.

Note that the plastic deformation stage islogically divided into 2D and 1D deformation sub-stages. HDG as a 2D material is plastically deformedduring the former stage occurring from 40 to 148%. Then, nanoscale cracks/pores separate HDGinto two pieces joined by a monatomic carbon chain(Fig. 5), and 1D deformation stage occurs which isrealized through elongation of the carbon chain. Thecrossover from 2D to 1D deformation regimes comesinto play at 148%. 1D plastic deformationprogresses until complete fracture of HDG -complete separation of HDG into two separatepieces (Fig. 6) – at strain-to-failure  234%.

5. CONCLUDING REMARKS

To summarize, with MD simulations, we haveexamined deformation and fracture processes inHDG under tensile load. HDG has thenanoscopically curved structure due to 5- and 7-discinations distributed with a high density in thisgraphene system (Figs. 1 and 2). It is found thatHDG exhibits the specific behavioral features owingto disclination-induced curvature. In particular, oursimulations revealed that HDG shows superplasticityspecified by strain-to-failure 234% (Fig. 7). Thekey reason of superplasticity is in the presence ofpre-existent disclinations that enhance generation

Fig. 7. Stress-strain dependence.

of new disclination dipoles and other disclinationconfigurations effectively carrying plastic flow ingraphene (Figs. 3 and 4).

Also, from the stress-strain dependencepresented in Fig. 7 it follows that HDG ischaracterized by both rather high elastic limit

el

40 % and tensile strength t 50 GPa. For

comparison, in the experiment [11], pristine graphenemembrane of micron-sized diameter shows

el 25%

and t 130 GPa. Thus, our simulations have

revealed both enhancement of the elastic limit anddegradation of the tensile strength of HDG, ascompared to pristine graphene.

The presented results are important forunderstanding the effects of disclination-producedcurvature on the mechanical properties of graphene.In the context discussed, of particular interest issuperplasticity exhibited by HDG. This highly plasticbehavior is contrasted to typical brittle behavior ofmost graphene structures. At the same time, giantplasticity has been observed in MD simulations oftensile tests with ultranarrow graphene nanoribbons[28] where free surface effects are highlypronounced. The results presented in this paper andthose presented in Ref. [28] are indicative of theintriguing (from both fundamental and appliedviewpoints) possibility to dramatically enhanceplasticity of graphene through insertion ofdisclinations into it and use of ultranarrow ribbongeometry, respectively.

ACKNOWLEDGEMENTS

This work was supported by the Russian ScienceFoundation (Project 14-29-00199). The simulationswere performed at Resource Center  “SimulationCenter of St. Petersburg State University”.

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